Frances O’Grady: ‘This is not about sovereignty; this is about saying there will be a level playing field and nobody will fall below this basic standard.’
Photograph: Stefan Wermuth/Reuters

Theresa May must give a clear commitment to match EU social protections after Brexit if voters are to trust her promise to put “ordinary working people” first, the TUC general secretary, Frances O’Grady, has said.

As the Conservatives put the final touches to their manifesto for the general election on 8 June, O’Grady, who represents almost 6 million working people, said the document should include a promise to ensure Brexit is not used as an excuse for a “race to the bottom”.

In particular, she would like to see the final Brexit deal that will determine how Britain trades with the EU in future include a promise not to undercut European social standards.

“This is not about sovereignty; this is about saying there will be a level playing field and nobody will fall below this basic standard,” she said.

“Now of course, Theresa May has already said that she won’t just protect rights, she will enhance them – so it should cause no problem whatsoever for the Conservative party to sign up to a commitment that British workers will not fall behind rights in other countries.”

That idea has already been included in plans for the talks by Brussels’ chief negotiator, Michel Barnier, after lobbying from trade unions. The European council’s negotiating guidelines say of any future trade deal with the UK: “It must ensure a level playing field, notably in terms of competition and state aid, and in this regard encompass safeguards against unfair competitive advantages through, inter alia, tax, social, environmental and regulatory measures and practices.”

O’Grady said: “I am pleased that in the EU negotiating guidelines it’s very clear about the need for a level playing field post-Brexit, and that that includes what they call social rights, and we call workers’ rights,” she said.

The Brexit secretary, David Davis, has said existing rights underpinned by the EU will be protected in the “great repeal bill” – the process for bringing EU rules and regulations into UK law.

O’Grady said they should go further: “They can guarantee it in the great repeal bill; they can also guarantee it in the deal. That is really important, because it is about what kind of investment we want to attract. Are we going to do it on the back of wanting to be the new Singapore? Or are we going to do it on the back of taking the high road to high productivity, high-skilled jobs, high performance?”

Without a clear commitment to match progress in the EU, O’Grady said, Britain would fall behind. “We know the EU is developing a new social pillar; there’s going to be new rights to paid parental leave – so they’re going to crack on; can Mrs May match it?”

Such a pledge would be anathema to some Brexiters in the Conservative party, however, who believe escaping what they regard as burdensome EU regulation, including on workers’ rights, would be one of the major benefits of leaving the trading bloc.

What does the election mean for Brexit and what does Brexit mean for the election?

It is unlikely that the result will affect Brexit, with both Tories and Labour saying they will enact the referendum result, though if Labour wins we might be more likely to see a “soft Brexit” as opposed to a hard one.

A number of MPs campaigned differently from the way their constituency voted, for example the Labour MP for Vauxhall, Kate Hoey, who backed Brexit, while only 22% of her constituents voted to leave. While nationally Labour campaigned for remain, many traditionally Labour constituencies voted to leave. How this plays out in the general election remains to be seen.

Rights at work have become an increasingly pressing political issue over recent years, as real take-home pay has stagnated, insecure, low-paid jobs have proliferated, and high-profile cases such as that of Sports Direct have shed light on exploitative practices.

George Osborne responded to the pressure by announcing a “real living wage” for the over-25s, but May has put “ordinary, working people” at the heart of her pitch to govern Britain, and the Conservatives have increasingly sought to portray themselves as the real “workers’ party”.

Labour has announced its manifesto will include 20 pledges to improve working life, including doubling paid paternity leave, scrapping employment tribunal fees, and making it easier for trade unions to organise in hard-to-reach workplaces.

The shadow Brexit secretary, Keir Starmer, has also said he would like to include a mechanism in domestic legislation to ensure workers’ rights keep pace with those in the EU in future.

O’Grady says May must now explain what she will do: “What’s going to be in that manifesto that gives people confidence that their worries are going to be addressed, and that this is going to be a party that recognises that one of the big challenges of our time is how we create better, more secure well-paid jobs?”

May set up a review, chaired by former New Labour adviser Matthew Taylor, to report on the 21st-century workplace. But O’Grady said, “I don’t think it’s going to be good enough at this stage to talk about reviewing things or developing things. I don’t think that’s going to cut much ice.”

She said acting to make people’s lives better at work would be consistent with the enthusiasm of one of May’s closest advisers, Nick Timothy, for the legacy of Joseph Chamberlain.

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“I was musing on this, because clearly her trusted team are inspired by Chamberlain, and I assume that inspires her too, and if you think about what Joseph Chamberlain did, and was committed to, it was about broadening the vote, giving working-class people a choice; it was about homes; and it was about making work healthier and safer, and compensating for people when it wasn’t. Those were the big, big social reforms – so I’m genuinely interested to see where Mrs May’s ambition lies in making Britain a better place for working people.”

“What is clear is it can’t be fiddling around the edges. We’ve got huge imbalances in our economy. We’ve got more and more wealth concentrated in London and the south-east; and in places like the north-east, two-thirds of all the new jobs created in the last five or six years have been casual jobs. And just families, feeling really worried.”

The TUC is not affiliated to a political party – though many of its member trade unions back Labour. Asked whether Labour could still win the general election, which Jeremy Corbyn has conceded is a “challenge on an historic scale”, O’Grady said: “Yes”.

She added that she would like to see the prime minister agree to face the Labour leader in a head-to-head television debate. “I think Jeremy is a really decent man, with strongly held principles, and what you see is what you get. He’s been tested in terms of the media. We don’t have a position on TV debates but it seems to me personally that politicians should be out there.”